Solve for $n$, $ \dfrac{n - 4}{5n^3} = \dfrac{6}{n^3} - \dfrac{5}{n^3} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $5n^3$ $n^3$ and $n^3$ The common denominator is $5n^3$ The denominator of the first term is already $5n^3$ , so we don't need to change it. To get $5n^3$ in the denominator of the second term, multiply it by $\frac{5}{5}$ $ \dfrac{6}{n^3} \times \dfrac{5}{5} = \dfrac{30}{5n^3} $ To get $5n^3$ in the denominator of the third term, multiply it by $\frac{5}{5}$ $ -\dfrac{5}{n^3} \times \dfrac{5}{5} = -\dfrac{25}{5n^3} $ This give us: $ \dfrac{n - 4}{5n^3} = \dfrac{30}{5n^3} - \dfrac{25}{5n^3} $ If we multiply both sides of the equation by $5n^3$ , we get: $ n - 4 = 30 - 25$ $ n - 4 = 5$ $ n = 9 $